"Freedom of speech is a privilege intended for educated professionals. It should be illegal for a high-school dropout to promote anti-government propaganda on his 5 dollar blog, if he cannot properly verify his statements."That is so preposterous a statement that I could not believe it would have been uttered by anyone with any awareness of basic 1st Amendment thinking. So I tracked down the YouTube video [edited April 2 to add link] from which the still picture was taken, and watched it, and of course she never actually utters those words in that grammatical order. Some of the words appear, but not in the way implied by the false quote.
For example, she does use the word "privilege", although she never says "Freedom of speech is a privilege". In fact, she's talking about privilege in the legal sense, a special exemption from certain kinds of legal obligations that would otherwise apply.
Consider "attorney-client privilege". There are circumstances in which a person may be legally required to answer questions truthfully, such as when testifying in court or being examined on an affidavit. Privileged communications, however, are exempt; your lawyer cannot be obliged at law to disclose things you tell her in connection with seeking legal advice. If you go to your lawyer to ask how you can hasten your rich uncle's death so you can inherit, and she tells you "Don't do it, because it's against the law," then you know that's not an option and you can obey the law. If your uncle then dies under suspicious circumstances that you actually had nothing to do with, the fact that you sought legal advice should not be used as evidence to bring you under suspicion. We want people to seek legal advice.
So what Ms. Feinstein was talking about here was whether or not there should be a similar sort of privilege for people who publish official secrets, and if so, what criteria there should be for someone who would enjoy that privilege. You can promote anti-government propaganda on your blog all you want, but if you publish actual secret documents, you might well be subject to criminal proceedings.
There's a difficult line to draw here. On the one hand, there is sometimes a legitimate state interest in secrecy (although I tend to suspect the state claims this interest more often than they should). Obviously, we do not want people to be able to publish the new names and locations of people in the witness protection program, and claim freedom of speech as their defence. People who expose legitimate secrets ought to face legal consequences, and people who come into possession of such stolen documents might well be legally compelled to say where they got them.
On the other hand, government secrecy always carries a great risk of protecting corruption and abuse of power. Sometimes the only defense against this is for a whistleblower to leak the information to the press, but if the reporter you give the documents to can be forced to reveal your identity, you're less likely to blow the whistle in the first place. So, because it might sometimes be in the public interest to facilitate such whistleblowing, maybe there ought to be a form of privilege for actual journalists to protect their sources. (Presumably, actual journalists will be bound by some form of professional ethics when they decide whether or not to publish something.)
Now, I am not saying anything about whether or not Senator Feinstein's position is an appropriate one. How much government secrecy there should be and how it should be protected is a complicated issue, and you can certainly disagree with Ms. Feinstein's approach to it. You can even use the strawman if you want, and say what you think her position is. But putting quotes around your own paraphrased (mis)interpretation of her position in order to imply that you're quoting her actual words? That is, in a word, lying.